Electric field (easy at least I thought so)

[Kalie]

The electric field strength 5.0 cm from a very long charged wire is 2000 N/C.
What is the electric field strength 10.0 cm from the wire?

Okay I thought that since the radius is double what it was before using the equation:

E= K*q*(r head)/(r^2)

I said that it decreases 1/4 and becomes 500.

Thats wrong. But obviously because I ignored r head...the vector thingy. But how do I apply it to the equation and solve for its new value?

Sigh...confused

 

[mjsd]

think about the symmetry... for a point charge the field is distributed in all direction (a spherical gaussian surface), for a line of charges (the lateral surface of a cylinder)... so in other words, you have used the wrong formula. Use Gauss's law to derive a new a formula (E as a fn of r)

 

[m2003]

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I would like to clarify that the electric field strength 5.0 cm from a very long charged wire is not solely determined by its distance from the wire, but also by the charge of the wire and the medium it is placed in. The equation you have mentioned, E= K*q*(r head)/(r^2), is the correct equation to use for calculating the electric field strength at a given distance from a charged wire. However, in order to solve for the new value at 10.0 cm, you would also need to know the charge of the wire and the direction of the electric field.

The vector notation, r head, represents the direction of the distance from the wire to the point where the electric field is being measured. This is important because the electric field is a vector quantity, meaning it has both magnitude and direction. So, in order to accurately calculate the new electric field strength at 10.0 cm, you would need to know the direction of the distance from the wire to the point.

Additionally, the electric field strength at a given distance from a charged wire does not necessarily decrease in a linear fashion. It depends on the geometry of the wire and the surrounding medium. So, it is not valid to simply divide the original value by 4 to get the new value at 10.0 cm.

In summary, to accurately calculate the electric field strength at a given distance from a charged wire, you would need to know the charge of the wire, the direction of the distance, and the geometry of the wire and surrounding medium. I hope this helps to clarify any confusion.